Maximizing profit. A company produces x units of product A and y units of product B (both in hundreds per month). The monthly profit equation (in thousands of dollars) is given by P ( x , y ) = − 4 x 2 + 4 x y − 3 y 2 + 4 x + 10 y + 81 (A) Find P x (1, 3) and interpret the results. (B) How many of each product should be produced each month to maximize profit? What is the maximum profit?
Maximizing profit. A company produces x units of product A and y units of product B (both in hundreds per month). The monthly profit equation (in thousands of dollars) is given by P ( x , y ) = − 4 x 2 + 4 x y − 3 y 2 + 4 x + 10 y + 81 (A) Find P x (1, 3) and interpret the results. (B) How many of each product should be produced each month to maximize profit? What is the maximum profit?
Solution Summary: The author explains how to obtain the value of P_x(1,3) and calculate the partial derivative of the above function with respect to x.
Maximizing profit. A company produces x units of product A and y units of product B (both in hundreds per month). The monthly profit equation (in thousands of dollars) is given by
P
(
x
,
y
)
=
−
4
x
2
+
4
x
y
−
3
y
2
+
4
x
+
10
y
+
81
(A) Find Px(1, 3) and interpret the results.
(B) How many of each product should be produced each month to maximize profit? What is the maximum profit?
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